The invention relates to the field of periodic dielectric structures, and in particular to such structures with complete or omnidirectional photonic band gaps.
Much research in recent years has been focused on photonic crystals: periodic dielectric (or metallic) structures with a photonic band gap (PBG), a range of frequencies in which light is forbidden to propagate. Photonic crystals provide an unprecedented degree of control over light, introducing the possibility of many novel optical devices and effects. One important area for potential applications is that of integrated optics; here, the band gap allows miniaturization to the ultimate wavelength scale while eliminating the inefficiencies and complexities caused by radiation losses in such devices.
Generally speaking, there have been two main categories of study regarding photonic-crystal systems for integrated optics: first, analyzing the phenomena and potential devices that a PBG makes possible; and second, figuring out how to realize these effects in practice. There is a need to bridge the gap between these two categories. It is therefore desirable to achieve a three-dimensional crystal, amenable to layer-by-layer lithographic fabrication, which permits the direct realization of theoretical results from two dimensions.
In order to understand PBG phenomena and to propose useful optical components that photonic crystals might make possible, researchers have often focused on two-dimensional systems. Working in two dimensions has many advantages, in addition to the substantial computational savings versus 3D. The electromagnetic fields are completely TE or TM polarized, with the electric or magnetic field, respectively, entirely in the plane. This reduces the vectorial Maxwell""s equations to a scalar problem in terms of the field (magnetic or electric, respectively) perpendicular to the plane. As a result of this scalar, two-dimensional nature, visualization and understanding of theory and simulation are greatly simplified. Band gaps are achieved with uncomplicated structures, and symmetries are obvious. Another attraction of two dimensions that is particularly relevant in device design: when trapping light in linear defects (waveguides) and point defects (microcavities), the fixed polarization and simple geometries make it easy to predict, analyze, and manipulate the character of the localized modes introduced by the defects.
In two dimensions, photonic band gaps have been shown to make possible a number of useful optical components, some of which are shown in FIGS. 1A-1D: sharp bends, efficient waveguide splitters and intersections, and channel-dropping filters. FIGS. 1A-1D are top views of block diagrams of photonic-crystal devices in a two-dimensional crystal (square lattice of dielectric rods in air), showing the TM electric field value. All four devices have essentially 100% transmission, with no reflections or losses. FIG. 1A shows a 90xc2x0 waveguide bend 100, FIG. 1B shows a channel-dropping filter 102, FIG. 1C shows an intersection 104 of two waveguides without crosstalk, and FIG. 1D shows a waveguide splitter/junction 106.
All of these devices are designed by combining a few well-understood elements (waveguides and cavities) and by employing general principles of resonance, symmetry, and coupled-mode theory. The attainable device characteristics are thereby known a priori, and minimal tuning is required to push the precise numerical results to the desired values. What makes all of this possible is the photonic band gap: it forces the light to exist only in one of a few states or channels, and transforms a problem with infinitely many directions of propagation into a one-dimensional system with a small number of variables. Although the same ideas can be then applied to conventional waveguides employing total internal reflection, the inevitable radiation losses of those systems spoil the perfection of the theory (and the devices). Such losses generally require ad hoc tuning to minimize, and greatly complicate the design, usage, and understanding of any component.
For example, consider the case of the waveguide bend in FIG. 1A. Because of the photonic band gap, light can do only one of two things when it hits the bend: go forward, or go back. The radiation that would plague any sharp bend in a conventional waveguide is completely absent, since light cannot propagate in the bulk crystal. Moreover, if the waveguide and bend region support only single-mode propagation, the problem can be described effectively as transmission through a one-dimensional potential well. If the bend/well is symmetric, a well-known result predicts resonant frequencies with 100% transmission, and nearly the exact transmission curve can be calculated via this model. Significantly, these predictions are independent of the exact crystal or waveguide structure, and depend only upon their symmetry and single-modality.
In order to realize two-dimensional photonic-crystal designs in three dimensions, one would ideally like to use the same 2D pattern for the 3D structure. That is, use a two-dimensionally-periodic slab, consisting of a two-dimensionally periodic dielectric structure with constant cross-section in the vertical direction and finite height, as depicted in FIGS. 2A and 2B for two typical structures. FIGS. 2A and 2B are perspective views of block diagrams of two-dimensionally-periodic slabs. By themselves, they can form photonic-crystal slabs, which use a combination of in-plane photonic band gaps and vertical index-guiding. FIG. 2A shows a triangular lattice 200 of dielectric rods 201 in air. FIG. 2B shows a triangular lattice 202 of air holes 203 in dielectric.
It will be appreciated that the exact shape of the rods/holes are of little importance; the key feature is their topology: a high/low dielectric region surrounded by low/high dielectric, respectively. In fact, such slabs form the building blocks of the new 3D crystal that is described herein.
With the slab alone, however, one encounters the obvious difficulty of how light is confined in the third dimension and the question of whether if one takes into account the third dimension, is there any longer a band gap. One possible answer to these questions, dubbed photonic-crystal slabs, uses index-guiding (total internal reflection) to confine light vertically. In this case, the higher index of the slab (compared to the material above and below) produces guided modes confined to the vicinity of the slab, and the periodicity creates a band gap where no guided modes exist. Although this is not a complete gap due to the presence of radiating modes at all frequencies (the light cone), it can be used to losslessly confine light in linear waveguides and to imperfectly trap light in resonant cavities.
The lack of a complete band gap leads to a number of difficulties, however. First, whenever translational symmetry is broken, e.g., by a bend or a cavity, radiation losses are inevitable. Although such losses can often be minimized, they must be continually taken into account, just as for conventional waveguides. A second limitation is that the need for waveguide modes to be index-guided, and thus to lie underneath the light line, produces a limited bandwidth and low group velocities in a periodic slab (compared to two-dimensional crystals or to conventional waveguides). Nevertheless, because of their relative ease of fabrication, slab structures continue to attract considerable experimental and theoretical attention. Another interesting system with somewhat different tradeoffs uses in-plane resonant modes above the light line, i.e., not guided, which more closely model the two-dimensional modes at the expense of large aspect ratios required everywhere to minimize radiation losses.
A full realization of a photonic band gap requires a crystal periodic in all three dimensions, and many such structures have been proposed. Some of the most attractive systems for integrated optics are planar-layer structures. These systems have piecewise-constant cross-sections, and can thus be fabricated in a layer-by-layer fashion using traditional micro-lithography. The fine control provided by lithography promises the ability to precisely place defects in the crystal in order to construct integrated optical devices. The planar-layer crystal that has been most commonly fabricated (with success even at micron lengthscales), is the layer-by-layer (or woodpile) structure, dielectric logs stacked in alternating perpendicular directions with a 4-layer period, forming an fcc crystal oriented in the 100 direction. However, this and other previous planar-layer structures lack rotational symmetry in any given plane, meaning that integrated optical networks will require defects to extend across multiple layers of the structures. Moreover, the nature of the defect modes so confined will have significant qualitative differences from those in two-dimensional crystals, because the dielectric structure where the mode resides does not resemble a 2D crystal. The one exception to this rule is the simple-cubic scaffold lattice, which has square-lattice symmetry in its cross sections, albeit with a small 6-7% gap.
Accordingly, the invention provides a photonic-crystal structure with a complete (omnidirectional) three-dimensional photonic band gap (PBG) and its potential application to integrated optics. The structure not only has a large band gap and is amenable to layer-by-layer litho-fabrication, but also introduces the feature of high-symmetry planar layers resembling two-dimensional photonic crystals. This feature enables integrated optical devices to be constructed by modification of only a single layer, and supports waveguide and resonant-cavity modes that strongly resemble the corresponding modes in the simpler and well-understood 2D systems.
In contrast to previous attempts to realize 2D crystals in 3D via finite-height slabs, however, the complete PBG of the invention eliminates the possibility of radiation losses. Thus, it provides a robust infrastructure within which to embed complex optical networks, combining elements such as compact filters, channel-drops, and waveguide bends/junctions that have previously been proposed in 2D photonic crystals.
In one exemplary embodiment of the invention there is provided a periodic dielectric structure having a three-dimensional photonic bandgap. The structure includes a plurality of stacked first and second two-dimensionally periodic slabs arranged in an alternating sequence. The first two-dimensionally periodic slabs comprising lower dielectric rods surrounded by higher dielectric material. The second two-dimensionally periodic slabs include higher dielectric rods surrounded by lower dielectric material. The rods of the first or second two-dimensionally periodic slabs are laterally offset from the rods of a nearest consecutive two-dimensionally periodic slab of the same type.